The statistical properties and possible causes of polar motion prediction errors

Wiesław Kosek(1) , Maciej Kalarus(2), Agnieszka Wnęk(1), Maria Zbylut-Górska(1)

(1) Environmental Engineering and Land Surveying, University of Agriculture in Krakow, Poland

(2) Space Research Centre, Polish Academy of Sciences, Warsaw, Poland

XXIX General Assembly, Honolulu, Hawaii - August 3 - 14, 2015

Future EOP data are neededFuture EOP data are needed to compute real time to compute real time transformation between the CRF and TRF. transformation between the CRF and TRF.

This transformation This transformation realized by predictions of x, y, UT1-UTC and a precesion-nutation extrapolation model is important for is important for the NASA Deep Space Network, which is an international the NASA Deep Space Network, which is an international network of antennas that supports: network of antennas that supports: - interplanetary spacecraft missions, - interplanetary spacecraft missions, - radio and radar astronomy observations, - radio and radar astronomy observations, - selected Earth-orbiting missions.- selected Earth-orbiting missions.

EOP Prediction – international cooperationEarth Orientation Parameters Prediction Comparison Campaign

(EOPPCC) (Oct. 2005 – Mar. 2008) [H. Schuh (Chair), W. Kosek, M. Kalarus] The goal: comparison of the EOP prediction results from different methods and input

data. 10 participants submitted weekly predictions.

IERS Working Group on Predictions (WGP) (Apr. 2006 – Oct. 2009) [W. Wooden (Chair), T. Van Dam (input data) , W. Kosek

(algorithms)] The goal: to show advantages and disadvantages of different prediction algorithms and

quality of different input data.

IERS Workshop on EOP Combination and Prediction (Warsaw, 19-21 October 2009) [W. Kosek, B. Wooden (Chairs)] This Workshop generated about 20 recommendations related to observations, analysis

and prediction of the EOPs.

Earth Orientation Parameters Combination of Prediction Pilot Project (EOPCPPP)

(Oct. 2010 – now ) [Chair: B. Luzum, co-chair: W. Kosek], The goal: To determine the feasibility and benefits of combining EOP predictions on a daily

basis and to determine the best algorithms for EOP predictions combinations. 9 participants submitted daily predictions.

DATA

• x, y from IERS: EOPC04_IAU2000.62-now (1962.0 - now), Δt = 1 day, http://hpiers.obspm.fr/iers/eop/eopc04_05/,

• Long term earth orientation data EOP C01 IAU2000 (1890 - now), Δt = 0.05 years http://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html

• x,y pole coordinates data prediction results from different participants of the Earth Orientation Parameters Combination of Prediction Pilot Project (Oct.2010 – now), Δt = 1 day, http://www.cbk.waw.pl/eopcppp/ http://maia.usno.navy.mil/eopcppp/eopcppp.html

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

years

-500

-400

-300

-200

-100

0

100

200

300

400

500

perio

d (d

ays)

arcsec

FTBPF am plitude spectrum : x-iy lambda=0.0002

-0

0.05

0.1

0.15

0.2

0.25

Time variable amplitude spectrum of complex-valued pole coordinates data computed by the Fourier transform band pass filter

The participants of the EOPCPPP and their contribution to x,y predictions.

Participant InstituteTotal number of x,y predictions

Brian Luzum (BL) U.S. Naval Observatory, Washington DC, USA

1630 and1083 combined

predictions until Dec 2013

Daniel Gambis (DG) Paris Observatory, Paris, France 1740

Leonid Zotov (LZ)Sternberg Astronomical Institute of Moscow State University, Department of Gravimetry, Moscow, Russia

136013601360

Maciej Kalarus (MK) Space Research Centre, PAS, Warsaw, Poland 1591

Richard Gross (RG) Jet Propulsion Laboratory, Pasadena, California, USA 1663

Viktor Tissen (VT)Siberian Scientific Research Institute of Metrology and Siberian State Geodetic Academy, Russia

1667

Wiesław Kosek (WK) Space Research Centre, PAS, Warsaw, Poland 1782

Xu Xueqing (XX) Shanghai Astronomical Observatory, China 1532

Zinovy Malkin (ZM) Pulkovo Observatory, Russia 1777

90-day polar motion predictions at different starting prediction epochs in 2012 from different participants of the EOPCPPP

Standard deviation (SDE)

Mixxn

SDE pn

j jiobspred

jip

i ,...2,1,1

1

2

,,

Mixxn

pn

j

obspredji

pji ,...2,1,

11 ,,

p

ii

n

SDESDE

2)(ˆ

Mixxn

MAE pn

j

obspredji

pi ,...2,1,

11 ,

Mean absolute error (MAE)

pii n

SDEMAE

2

)(ˆ

MiSDE

xxn

SKEi

n

i jiobspred

jip

i

p

,...,2,1,

)(1

3

1

3,,

Skewness (SKE)

pi nSKE /6)(ˆ

MiSDE

xxn

KURi

n

i jiobspred

jip

i

p

,...,2,1,

)(1

4

1

4,,

Kurtosis (KUR)

pi nKUR /24)(ˆ

Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Brian Luzum.

SDEarcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03 MAE

arcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03

SKEW NESS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

-2.0-1.5-1.0-0.50.00.51.01.52.0

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0123456789

10 KURTOSIS

x, y

Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Viktor Tissen.

SDEarcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03MAE

arcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03

SKEW NESS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

-2.0-1.5-1.0-0.50.00.51.01.52.0 KURTOSIS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0123456789

10

x, y

Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Zinovy Malkin.

SDEarcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03MAE

arcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03

SKEW NESS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

-2.0-1.5-1.0-0.50.00.51.01.52.0

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0123456789

10 KURTOSIS

x, y

Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Wieslaw Kosek.

SDEarcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03MAE

arcsec

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0.00

0.01

0.02

0.03

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0123456789

10 KURTOSISSKEW NESS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

-2.0-1.5-1.0-0.50.00.51.01.52.0

x, y

Mean absolute error (MAE), standard deviation (SDE), skewness and kurtosis together with their error bars of x (blue), y (red) predictions computed by Maciej Kalarus.

SDEarcsec

0 10 20 30 40 50 60 70 80 900.00

0.01

0.02

0.03 MAE

arcsec

0 10 20 30 40 50 60 70 80 900.00

0.01

0.02

0.03

SKEW NESS

0 10 20 30 40 50 60 70 80 90

days in the fu ture

-2.0-1.5-1.0-0.50.00.51.01.52.0

0 10 20 30 40 50 60 70 80 90

days in the fu ture

0123456789

10 KURTOSIS

x, y

The differences between the IERS x,y pole coordinates data and their LS+AR 90-day predictions

and time series of these differences for one (purple) and two (green) weeks in the future.

1990 1995 2000 2005 2010 2015

years

-0.02

-0.01

0

0.01

0.02

arcsec y 1990 1995 2000 2005 2010 2015-0.02

-0.01

0

0.01

0.02

arcsec x

Cor_coef=0.595 ± 0.022

Cor_coef=0.549 ± 0.022

020406080

-0.06

-0.04

-0.02

0.00

0.02

0.04

1990 1995 2000 2005 2010 2015years

020406080

d

ays

in t

he

fu

ture

a rcsec

x

y

The mean FTBPF amplitude spectra (λ=0.0003) of the differences between the IERS x-iy pole coordinates data and their LS+AR predictions at 2, 4 and 8 weeks in the future

-800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800period (days)

0

0.001

0.002

0.003

0.004

0.005

0.006

2 w eeks

4 w eeks

8 w eeks

arcsec

Time variable FTBPF amplitude spectra (λ=0.001) of the differences between the IERS x-iy pole coordinates data and their LS+AR predictions at 1 day and 1, 2, 4 weeks in the future

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012-800

-400

0

400

800

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

prediction d ifferences at 1 w eek in the future arcsec

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012-800

-400

0

400

800

p

erio

d (d

ays)

-00.00040.00080.00120.00160.0020.00240.00280.0032

prediction d ifferences at 2 weeks in the future arcsec

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012years

-800

-400

0

400

800

-00.0010.0020.0030.0040.0050.0060.007

prediction d ifferences at 4 w eeks in the future arcsec

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012-800-600-400-200

0200400600800

prediction d ifferences at 1 day in the future

-0

1E-005

2E-005

3E-005

4E-005

5E-005

arcsec

Amplitudes and phases of the Chandler (green) and Annual (x-blue, y-red) oscillations computed by combination of complex demodulation and the Fourier transform band pass filter

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 20100

0.1

0.2

0.3 C h x,y

An x

An y

Am plitudearcsec

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010years

-160-140-120-100

-80-60-40-20

020406080

100120140160

C h x,y

An xAn y

Phaseo

First differences of amplitudes (x-red, y-orange) and the products of amplitudes and phase differences (x-navy blue, y-blue) of the Chandler, annual and semi-annual oscillations computed by the CD+FTLPF combination.

1960 1970 1980 1990 2000 2010-0.0003-0.0002-0.0001

00.00010.00020.0003 Chandler xdA ydAarcsec/day

1960 1970 1980 1990 2000 2010-0.0003-0.0002-0.0001

00.00010.00020.0003 Chandler xAdf yAdfarcsec/day

1960 1970 1980 1990 2000 2010-0.0003-0.0002-0.0001

00.00010.00020.0003 Annual xAdf yAdfarcsec/day

1960 1970 1980 1990 2000 2010-0.0003-0.0002-0.0001

00.00010.00020.0003 Annual xdA ydAarcsec/day

1960 1970 1980 1990 2000 2010years

-0 .00003

-0.00002

-0.00001

0.00000

0.00001

0.00002

0.00003 Semi-annual xdA ydAarcsec/day

1960 1970 1980 1990 2000 2010years

-0.00003

-0.00002

-0.00001

0.00000

0.00001

0.00002

0.00003 Semi-annual xAdf yAdf arcsec/day

The skewness and kurtosic values of the differences between pole coordinates data and their predictions for different prediction lengths and for different participants of the Earth Orientation Parameters Combination of Prediction Pilot Project are close to 0 and 3, respectively which means that they follow normal distribution.

The increase of the differences between pole coordinates data and their prediction with the prediction length is caused by mismodelling of the irregular Chandler and annual oscillations in the LS+AR forecast models.

CONCLUSIONS